Question

Which represents the inverse of the function f(x) = 4x?

Answer 1

Answer: D)  h(x) = (1/4)x

This is the same as h(x) = x/4

In decimal form, it would be h(x) = 0.25x

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Explanation:

Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x

To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x

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Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y

f(x) = 4x

y = 4x

x = 4y

4y = x

y = x/4

h(x) = x/4

We end up with the same result as before.

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Extra info:

For any real number x, the following two equations are true

h( f(x) ) = x

f( h(x) ) = x